Issue with 2D Shrinkwrap (Circle onto Cross)
Make sure both shapes have a height and faces with area, so that Shrinkwrap modifier as normals on which to operate in.

Make sure you circle is big enough to encompass the whole cross.

Make sure your cross is high enough to cover all the circle height.

The point here is to guarantee all face normals encounter the other object operand. If you wish to have 2D shapes you can then after applyinf the modifier remove undesired faces and make them an edge wireframe only.

Change the Shrinkwrap modifier to Project mode, and the Direction to Negative. That should do it